Thermal oxidation is a process that converts silicon at the wafer surface into silicon dioxide. The reaction of oxygen with silicon causes silicon dioxide to develop at the surface, whilst also penetrating the silicon wafer. The final oxide is appropriately 56% above and 44% below the original surface. Modeling of thermal oxidation has a tradition dating back to the late 60's when the Deal-Grove model was developed, which is still used in modern simulators. The model is based on two parameters, the linear and parabolic rate constants, in which all the physics of the oxidation process are included.
Recently, it has been suggested that the growth of silicon dioxide can be described using the Navier-Stokes equation, which describe the motion of fluid substances, or substances with flow. Combined with this theory, the growth of silicon dioxide can be modeled as the movement of two boundaries that both originate at the wafer surface. One boundary penetrates the silicon wafer with a negative velocity, while the second moves above the original wafer surface and is assigned a positive velocity. The simulation of a moving boundary has been developed at this institute by O. Ertl in his work on describing the topography changing processes for Micro-Electro-Mechanical Systems (MEMS) manufacturing using the level set method.
The level set method is a technique that represents the moving boundary as the zero level set of an implicit function. The evolution of this function with time is calculated by solving the level set equation. A very efficient existing simulator uses the sparse-field method with Hierarchical Run-Length-Encoding (HRLE). The advantages of the existing topography simulator will be inherited by the thermal oxidation simulator. The goal is to model the simulation of oxide growth, stress sources, and various three-dimensional effects in an efficient 3D simulator using the level-set method and the Navier-Stokes equation.